Abstract
A pharmacodynamic model introduced earlier in the literature for in silico prediction of rifampicin-induced CYP3A4 enzyme production is described and some aspects of the involved curve-fitting based parameter estimation are discussed. Validation with our own laboratory data shows that the quality of the fit is particularly sensitive with respect to an unknown parameter representing the concentration of the nuclear receptor PXR (pregnane X receptor). A detailed analysis of the influence of that parameter on the solution of the model’s system of ordinary differential equations is given and it is pointed out that some ingredients of the analysis might be useful for more general pharmacodynamic models. Numerical experiments are presented to illustrate the performance of related parameter estimation procedures based on least-squares minimization.
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References
D. Z. D’Argenio, A. Schumitzky, X. Wang: ADAPT 5 User’s Guide: Pharmacokinetic/Pharmacodynamic Systems Analysis Software. Biomedical Simulations Resource, Los Angeles, 2009, Available at https://doi.org/bmsr.usc.edu/software/adapt/users-guide/.
S. Dhillon, A. Kostrzewski, (eds.): Clinical Pharmacokinetics. Pharmaceutical Press, London, 2006.
J. Duintjer Tebbens, M. Azar, E. Friedmann, M. Lanzendörfer, P. Pávek: Mathematical models in the description of pregnane X receptor (PXR)-regulated cytochrome P450 enzyme induction. Int. J. Mol. Sci. 19(2018), 1785.
A. Funahashi, M. Morohashi, H. Kitano, N. Tanimura: CellDesigner: a process diagram editor for gene-regulatory and biochemical networks. BIOSILICO 1(2003), 159–162.
The GNU Fortran compiler. Available at https://doi.org/gcc.gnu.org/fortran/.
A. C. Hindmarsh: Large ordinary differential equation systems and software. Control Systems Magazine 2 (1982), 24–30.
A. C. Hindmarsh: ODEPACK, a systematized collection of ODE solvers. Scientific Computing 1982 (R. S. Stepleman et al., eds.). IMACS Transactions on Scientific Computation I, North-Holland Publishing, Amsterdam, 1983, pp. 55–64.
H. M. Jones, K. Rowland-Yeo: Basic Concepts in Physiologically Based Pharmacokinetic Modeling in Drug Discovery and Development. CPT: Pharmacometrics & Systems Pharmacology 2 (2013), Article ID e63, 12 pages.
N. S. Luke, M. J. DeVito, I. Shah, H. A. El-Masri: Development of a quantitative model of pregnane X receptor (PXR) mediated xenobiotic metabolizing enzyme induction. Bull. Math. Biol. 72 (2010), 1799–1819.
L. Lukšan, M. Tůma, C. Matonoha, J. Vlček, N. Ramešová, M. Šiška, J. Hartman: UFO 2017. Interactive System for Universal Functional Optimization. Technical Report V-1252, Institute for Computer Science CAS, Praha, 2017. Available at https://doi.org/www.cs.cas.cz/luksan/ufo.html.
D. J. Lunn, N. Best, A. Thomas, J. Wakefield, D. J. Spiegelhalter: Bayesian analysis of population PK/PD models: General concepts and software. J. Pharmacokinetics Pharmacodynamics 29 (2002), 271–307.
MATLAB. Mathworks, Inc., 2018. Available at https://doi.org/www.mathworks.com/products/matlab.html.
C. Moler, C. Van Loan: Nineteen dubious ways to compute the exponential of a matrix, twenty-five years later. SIAM Rev. 45 (2003), 3–49.
J. A. Nelder, R. Mead: A simplex method for function minimization. Computer J. 4 (1965), 308–313.
NONMEM 7.3. ICON, Inc., 1990–2016. Available at https://doi.org/www.iconplc.com/innovation/nonmem/.
L. Petzold: Automatic selection of methods for solving stiff and nonstiff systems of ordinary diferential equations. SIAM J. Sci. Stat. Comput. 4 (1983), 136–148.
L. Shargel, A. B. C. Yu: Applied Biopharmaceutics & Pharmacokinetics. McGraw-Hill Education, New York, 2016.
Simcyp simulator. Certara, 2012. Available at https://doi.org/www.certara.com/software/.
J. W. Spruill, W. E. Wade, T. J. DiPiro, A. R. Blouin, M. J. Pruemer: Concepts in Clinical Pharmacokinetics. American Society of Health-System Pharmacists, Bethesda, 2014.
P. Zhao, M. Rowland, S.-M. Huang: Best practice in the use of physiologically based pharmacokinetic modeling and simulation to address clinical pharmacology regulatory questions. Clinical Pharmacology & Therapeutics 92 (2012), 17–20.
Z. Zheng, P. S. Stewart: Penetration of rifampin through staphylococcus epidermidis biofilms. Antimicrob. Agents Chemoter 46 (2002), 900–903.
Acknowledgement
We would like to thank Prof. Petr Pávek for the laboratory experiments described in this manuscript; they were performed under his supervision and in his laboratory at the Faculty of Pharmacy of Charles university in Hradec Králové.
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The work of Jurjen Duintjer Tebbens and Ctirad Matonoha was supported by the long-term strategic development financing of the Institute of Computer Science (RVO: 67985807) of the Czech Academy of Sciences. The work of Jurjen Duintjer Tebbens was also supported by the Czech science funding agency (GACR 17-06841S). The work of Andreas Matthios was supported by the grant agency of Charles University project GAUK 110/50/85003 and by SVV 260 414. The work of Štěpán Papáček was supported by the Ministry of Education, Youth and Sports of the Czech Republic — projects “CENAKVA” (No. CZ.1.05/2.1.00/01.0024), “CENAKVA II” (No. LO1205 under the NPU I program) and The CENAKVA Centre Development (No. CZ.1.05/2.1.00/19.0380)
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Duintjer Tebbens, J., Matonoha, C., Matthios, A. et al. On parameter estimation in an in vitro compartmental model for drug-induced enzyme production in pharmacotherapy. Appl Math 64, 253–277 (2019). https://doi.org/10.21136/AM.2019.0284-18
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DOI: https://doi.org/10.21136/AM.2019.0284-18